Tel and I have been going back and forth in the comments… He pointed out that if inventory grows at 2% forever (along with final sales), then GDP growth is a constant 2%. But be careful, what’s going on is that a constant 2% growth in inventories implies a constant 2% growth in the *change* in inventories, which is the relevant issue.

Below the first example shows what Tel is talking about, but the next two show what I am warning about. Note that inventory growth converges to 2% from both ends, even though GDP growth is a constant 2%.

I just remembered that if all you know is the second derivative f”(t) but you don’t know the original function f(t) then you can use a double integration to find f(t) but the answer is not unique… knowledge of the initial conditions of the system would be required to find a unique answer.

I think the biggest source of confusion is that the standard accounting identity for GDP includes consumption, which draws our attention away from production, which is what we’re actually trying to measure. In other words, GDP measures the *production* of final goods, and consumption is just the way to get there.

To arrive at production, we start with consumption and then add the amount of final goods that were produced but not consumed. This isn’t *wrong*. But it is confusing, as this whole episode shows.

One can imagine GDP accounting identities that don’t fall into this confusing trap. Ones that only look at production of final goods. Don’t look at consumption – that’s a distraction. Don’t look at inventory balances or their changes – that’s a distraction. Only look at production. The practical challenges of actually calculating GDP this way are probably to high to make this literally possible, but it’s helpful to at least think about.

Imagine if we treated the investment portion of GDP the way we treat consumption. In order to calculate investment, we would start with depreciation (or capital consumption), and then adjust depreciation by the change in capital stock. Again, this wouldn’t be *wrong*, but it’s obvious how this would cloud our thinking. We might start to worry about our machines not depreciating quickly enough, and become dismayed when higher production is caused by increases in our capital stock.